Non-porous solids

Isotherms of Type 111 and Type V, which are the subject of Chapter 5, seem to be characteristic of systems where the adsorbent-adsorbate interaction is unusually weak, and are much less common than those of the other three types. Type III isotherms are indicative of a non-porous solid, and some halting steps have been taken towards their use for the estimation of specific surface but Type V isotherms, which betoken the presence of porosity, offer little if any scope at present for the evaluation of either surface area or pore size distribution. 

The physical adsorption of gases by non-porous solids, in the vast majority of cases, gives rise to a Type II isotherm. From the Type II isotherm of a given gas on a particular solid it is possible in principle to derive a value of the monolayer capacity of the solid, which in turn can be used to calculate the specific surface of the solid. The monolayer capacity is defined as the amount of adsorbate which can be accommodated in a completely filled, single molecular layer—a monolayer—on the surface of unit mass (1 g) of the solid. It is related to the specific surface area A, the surface area of 1 g of the solid, by the simple equation... 

It follows therefore that the specific surface of a mesoporous solid can be determined by the BET method (or from Point B) in just the same way as that of a non-porous solid. It is interesting, though not really surprising, that monolayer formation occurs by the same mechanism whether the surface is wholly external (Type II isotherm) or is largely located on the walls of mesopores (Type IV isotherm). Since the adsorption field falls off fairly rapidly with distance from the surface, the building up of the monolayer should not be affected by the presence of a neighbouring surface which, as in a mesopore, is situated at a distance large compared with the size of a molecule. 

Any interpretation of the Type I isotherm must account for the fact that the uptake does not increase continuously as in the Type II isotherm, but comes to a limiting value manifested in the plateau BC (Fig. 4.1). According to the earlier, classical view, this limit exists because the pores are so narrow that they cannot accommodate more than a single molecular layer on their walls the plateau thus corresponds to the completion of the monolayer. The shape of the isotherm was explained in terms of the Langmuir model, even though this had initially been set up for an open surface, i.e. a non-porous solid. The Type I isotherm was therefore assumed to conform to the Langmuir equation already referred to, viz. 

DRYING OF A NON-POROUS SOLID A WATER LAYER EVAPORATES FIRST... 

Mg of dry mass of a non-porous solid is dried under constant drying conditions in an air stream flowing at 0.75 m/s. The area of surface drying is 55 m2. If the initial rate of drying is 0.3 g/m2s, how long will it take to dry the material from 0.15 to 0.025 kg water/kg dry solid The critical moisture content of the material may be taken as 0.125 kg water/kg dry solid. If the air velocity were increased to 4.0 m/s, what would be the anticipated saving in time if the process were surface-evaporation controlled ... 

The advantage of equation 17.14 is that it may be fitted to all known shapes of adsorption isotherm. In 1938, a classification of isotherms was proposed which consisted of the five shapes shown in Figure 17.5 which is taken from the work of Brunauer et alSu Only gas-solid systems provide examples of all the shapes, and not all occur frequently. It is not possible to predict the shape of an isotherm for a given system, although it has been observed that some shapes are often associated with a particular adsorbent or adsorbate properties. Charcoal, with pores just a few molecules in diameter, almost always gives a Type I isotherm. A non-porous solid is likely to give a Type II isotherm. If the cohesive forces between adsorbate molecules are greater than the adhesive forces between adsorbate and adsorbent, a Type V isotherm is likely to be obtained for a porous adsorbent and a Type III isotherm for a non-porous one. 

The assumption usually made is that the ratio Fu /Sbet has the same value at a given relative pressure independent of the solid. A plot therefore of t versus P/Pq should give the same curve for any non-porous solid (see Fig. 8.6). In fact, plots of the number of adsorbed layers versus P/Pq show some discrepancies which for the analysis of large pores is not significant. Therefore, the Halsey equation can be used for the statistical thickness in that application. However, for micropore analysis, a statistical thickness must be taken from a t versus P/Pq curve that has approximately the same BET C value as the test sample. The unavailability of t versus P/Pq plots on numerous surfaces with various C values would make the MP method of passing interest were it not for the fact that t can be calculated from equation (8.36). This implies that surface area can be accurately measured on microporous samples. Brunauer points out that in most instances the BET equation does correctly measure the micropore surface area. 

The subsequent explosion of array technologies has been sparked by two key inno-vations. The first is the use of non-porous solid support, such as glass, which has facilitated the miniaturization of the array and the development of fluorescence-hybridization detection (16, 17, 18). The second critical iimovation has been the development of methods for high-density spatial synthesis of oligonucleotides, which allows the analysis of thousands of genes at the same time. Because DNA cannot bind directly to the glass, the surface is first treated with silane to covalently attach reactive amine, aldehyde, or epoxies groups that allow stable attachment of DNA, proteins, and other molecules. 

The zirconia sensor operates primarily on the principle of a concentration cell. It consists of a non-porous solid electrolyte layer fabricated from zirconia stabilized with yttria or calcia and exhibits high oxygen ion mobility. This layer is sandwiched between two porous and electrically conductive electrodes. 

In one of the most common sensors, the non-porous solid electrolyte layers takes the form of a crucible closed at one end so that air used as a reference gas can be introduced into the interior of the crucible while the outside of the crucible is exposed to the exhaust gas. A schematic drawing and E versus the air-fuel ratio curve for this sensor are shown in Figure 1. E is the electromotive force (EMF) between the two electrodes in accordance with the Nemst equation ... 

Type II isotherms (e.g. nitrogen on silica gel at 77 K) are frequently encountered, and represent multilayer physical adsorption on non-porous solids. They are often referred to as sigmoid isotherms. For such solids, point B represents the formation of an adsorbed monolayer. Physical adsorption on microporous solids can also result in type II isotherms. In this case, point B represents both monolayer adsorption on the surface as a whole and condensation in the fine pores. The remainder of the curve represents multilayer adsorption as for non-porous solids. 

The theory of Brunauer, Emmett and Teller167 is an extension of the Langmuir treatment to allow for multilayer adsorption on non-porous solid surfaces. The BET equation is derived by balancing the rates of evaporation and condensation for the various adsorbed molecular layers, and is based on the simplifying assumption that a characteristic heat of adsorption A Hi applies to the first monolayer, while the heat of liquefaction, AHL, of the vapour in question applies to adsorption in the second and subsequent molecular layers. The equation is usually written in the form... 

Use the Kelvin equation to calculate the pore radius which corresponds to capillary condensation of nitrogen at 77 K and a relative pressure of 0.5. Allow for multilayer adsorption on the pore wall by taking the thickness of the adsorbed layer on a non-porous solid as 0.65 nm at this relative pressure. List the assumptions upon which this calculation is based. For nitrogen at 77 K, the surface tension is 8.85 mN m-1 and the molar volume is 34.7 cm3 mol-1. 

The Langmuir and BET equations work well with non-porous solids, but not as well for porous solids because the pores influence the local numbers of adsorption layers formed. Nevertheless, by using adsorption gases of different molecular size or by varying the temperature, pores of different size will be accessible to the adsorbing... 

For non-porous solids the particle density is equal to the true, skeletal, or absolute density, Pabs which can be measured using either a specific gravity bottle or air pycnometer ... 

POMs/HPA themselves are usually non-porous solids, with surface area less than 10 m2/g and low decomposition temperatures. Therefore, they have limited surface sites for surface-catalysed reactions. A number of attempts have been made to disperse POMs on inert supports, with the intention of effectively increasing the number of accessible active catalytic sites. A number of materials have been used as solid supports for the dispersion of HPA, for example silica, carbon, zirconia, alumina, and porous silica. 

The low-coverage energy data for the adsorption of n-hexane and benzene on various non-porous solids in Table 1.4 illustrate the importance of the surface structure of the adsorbent and the nature of the adsorptive. Since n-hexane is a non-polar molecule, Em > Esp, and therefore the value of E0 is dependent on the overall dispersion forces and hence on the density of the force centres in the outer part of the adsorbent (i.e. its surface structure). Dehydroxylation of a silica surface involves very little change in surface structure and therefore no significant difference in the value of E0 for n-hexane. However, replacement of the surface hydroxyls by alkylsilyl groups... 

Stoeckli (1993) has pointed out that the Dubinin-Astakhov equation (Equation (4.45)) can be derived from Equation (4.52), but McEnaney (1988) and others (e.g. Jaroniec et al. 1997) have drawn attention to the difficulty in arriving at an unambiguous interpretation of the energy distribution function. Indeed, Stoeckli et al. (1998) have now pointed out that Equation (4.45) can be usefully applied to a number of adsorption isotherms on non-porous solids. A comprehensive review of the significance and application of Equation (4.52) is given by Rudzinski and Everett (1992). 

The most straightforward form of as-plot is Type 11(a) in Figure 6.1, which is for a typical Type II isotherm with a moderate value of C ( 100). The extensive range of linearity and the zero intercept are the result of unrestricted monolayer-multilayer adsorption on a non-porous solid of very similar surface structure to that of the reference material. In this case the shapes of the experimental and standard isotherms are virtually identical and therefore the slope of the as-plot is directly proportional to the ratio of the surface areas, a(S)/aref. Thus, if the value of aKl is already known, it is a simple matter to calculate atest, which we denote a(S) to indicate it is calculated by the as-method. 

Less favorable is the situation with analyses of obtained data, viz. the most common cases of solids containing both micro- and meso-pores. Here the Brunauer-Emmet-Teller (BET) isotherm is nearly always incorrectly applied. The t-plot method [1] is only of limited applicability because it requires knowledge of adsorption isotherms on non-porous solids of the same chemical nature as the measured sample (master isotherm). Only recently it was shown in this Laboratory [2] that an extension of BET isotherm together with non-linear parameter fitting could solve this problem. 

The calculated volumes of micropores resulting from experimentally determined enthalpies of immersion into different liquids, when computed as for a non-porous solid, are usually higher (indicating that the energy attributed to the adsorption of a unit amount of immersion liquid molecules was too low), than the respective values from calculations, in which additional energy effects (caused by the presence of narrow micropores, where primary adsorption processes can occur) were taken into account. Figure 3... 

Replacement of the fine by the coarse fraction (the right-hand side of the diagram) appears at first as the addition of a compact non-porous solid, since the voids between the large particles are completely filled with the finer fraction. The total volume therefore changes according to the straight line tending towards the solid phase volume (line DA). 

Evaluation of the interaction of the API with water is an important and essential pre-formulation activity. For the purposes of our discussion, we will assume (/) the API of interest is a non-porous solid, (//) the API does not form a non-stoichiometric hydrate, and ( 7/) non-aqueous solvates of the API will not be considered for development. If these issues are of interest, they are addressed in the literature (35). 

The textural properties of the hybrid materials are also strongly dependent upon the hydrolysis conditions and the nature of the linker. After hydrolysis in a homogeneous medium, nitrogen adsorption and TEM measurements indicate the formation of non-porous solids with BET specific surface areas lower than 7 m except for 2g. Variation of the precursor concentration does not strongly affect these values. In contrast, hydrolysis under microemulsion conditions leads to a significant increase in the specific surface areas, mainly in the case of the flexible alkylene linker (Table 3.2.5). 

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